Fast real-time time-dependent hybrid functional calculations with the parallel transport gauge and the adaptively compressed exchange formulation

Abstract

We present a new method to accelerate real-time time-dependent density functional theory (rt-TDDFT) calculations with hybrid exchange–correlation functionals. In the context of a large basis set such as planewaves and real space grids, the main computational bottleneck for large scale calculations is the application of the Fock exchange operator to the time-dependent orbitals. Our main goal is to reduce the frequency of applying the Fock exchange operator, without loss of accuracy. We achieve this by combining the recently developed parallel transport (PT) gauge formalism (Jia et al. J. Chem. Theory Comput. 2018) and the adaptively compressed exchange operator (ACE) formalism (Lin, J. Chem. Theory Comput. 2016). The PT gauge yields the slowest possible dynamics among all choices of gauge. When coupled with implicit time integrators such as the Crank–Nicolson (CN) scheme, the resulting PT–CN scheme can significantly increase the time step from sub-attoseconds to 10−100 attoseconds. At each time step tn, PT–CN requires the self-consistent solution of the orbitals at time tn+1. We use ACE to delay the update of the Fock exchange operator in this nonlinear system, while maintaining the same self-consistent solution. We verify the performance of the resulting PT–CN–ACE method by computing the absorption spectrum of a benzene molecule and the response of bulk silicon systems to an ultrafast laser pulse, using the planewave basis set and the HSE exchange–correlation functional. We report the strong and weak scaling of the PT–CN–ACE method for silicon systems ranging from 32 to 1024 atoms, on a parallel computer with up to 2048 computational cores. Compared to standard explicit time integrators such as the 4th order Runge–Kutta method (RK4), we find that the PT–CN–ACE can reduce the frequency of the Fock exchange operator application by nearly 70 times, and the thus reduce the overall wall clock time by 46 times for the system with 1024 atoms. Hence our work enables hybrid functional rt-TDDFT calculations to be routinely performed with a large basis set for the first time.